For the production or optimization of spectacle lenses, in particular of individual spectacle lenses, each spectacle lens is manufactured such that the best possible correction of a refractive error of the respective eye of the spectacle wearer is obtained for each desired direction of sight or each desired object point. In general, a spectacle lens is said to be fully corrective for a given direction of sight if the values sphere, cylinder, and axis of the wavefront upon passing the vertex sphere match with the values for sphere, cylinder, and axis. However, a full correction for all directions of sight at the same time is normally not possible. Therefore, the spectacle lenses are manufactured such that they achieve a good correction of visual defects of the eye and only small aberrations especially in central visual regions, while larger aberrations are permitted in peripheral regions. These aberrations depend on the type and scope of the necessary corrections as well as on the position of the spectacle lens, i.e. the respective visual point.
In particular for a correction of an astigmatic refraction of an eye, in addition to knowing the amount of the astigmatic refraction, i.e. the value of the cylinder, the axial position thereof is decisive as well. In order to be able to correct an astigmatic refraction of the eye, these values are therefore measured for the eye to be corrected while the eye is in a measurement position or reference direction of sight, in particular the zero direction of sight. Here, preferably a coordinate system is specified, and the axial position of the astigmatic refraction with respect to this coordinate system is determined. The amount of the astigmatism can be indicated as the difference of the main refractive powers. The coordinate system may be a Cartesian coordinate system with the axes ex, ey, and ez, its point of origin particularly being in the ocular center of rotation of the eye to be corrected. The axis ez is preferably parallel to the reference direction of sight, in particular to the zero direction of sight, and is oriented in the direction of the main ray. Preferably, the axis ez is a horizontal axis, which with respect to the eye faces backward in the zero direction of sight, i.e. in the direction of the light ray. The axis ex runs e.g. horizontally and perpendicularly to the axis ez, in particular perpendicularly to the reference direction of sight or zero direction of sight. Finally, the axis ey runs perpendicularly to the two other axes and is in particular vertically oriented upward. Thus, the three axes ex, ey, and ez for example form a base coordinate system, in which also the axial position of an astigmatism to be corrected can be described.
When looking through a spectacle lens, the eye pair continuously performs eye movements, whereby the visual points change within the spectacle lens. Thus, eye movements always result in changes of the imaging properties, in particular of the aberrations for the spectacle lens. Furthermore, during eye movements, each eye performs a torsion about the momentary axis of the direction of sight, which in particular depends on the direction of sight itself. In the case of an astigmatic refraction of the eye, this often leads to an unsatisfactory correction of the astigmatism especially in the near zone.